By definition, pre-you only has access to the coin's probability distribution, while you have access to the result of the coin flip. Surely you don't mean to say that's the same thing?

From the perspective of a non-superintelligence, Omega's prediction abilities are indistinguishable from magic. Human beings can't tell what they "imply." Trying to figure out the implications with a primate brain will only get you into a paradox like claiming a fact is the same as a probability distribution. All we can reasonably do is stipulate Omega's abilities needed to make the problem work and no further.